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Write Date : 15-09-30 08:48
What is a Function 2?
 Writer : 관리자
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Piecewise Functions

A Function Can be in Pieces

We can create functions that behave differently based on the input (x) value.

Piecewise Function

A function made up of 3 pieces

Example:

  • when x is less than 2, it gives x2,
  • when x is exactly 2 it gives 6
  • when x is more than 2 and less than or equal to 6 it gives the line 10-x

It looks like this:

Piecewise Function

(a solid dot means "including",
an open dot means "not including")

And this is how we write it:

Piecewise Function

The Domain (all the values that can go into the function) is all Real Numbers up to and including 6, which we can write like this:

Dom(f) = (-∞, 6] (using Interval Notation)

Dom(f) = {x member of Reals | x ≤ 6} (using Set Builder Notation)

And here are some example values:

XY
-416
-24
00
11
26
37

Example: Here is another piecewise function:

which looks like:

What is h(-1)?x is ≤ 1, so we use h(x) = 2, so h(-1) = 2
What is h(1)?x is ≤ 1, so we use h(x) = 2, so h(1) = 2
What is h(4)?x is > 1, so we use h(x) = x, so h(4) = 4

Piecewise functions let us make functions that do anything we want!

Example: A Doctor's fee is based on the length of time.

  • Up to 6 minutes costs $50
  • Over 6 to 15 minutes costs $80
  • Over 15 minutes costs $80 plus $5 per minute above 15 minutes

Which we can write like this:

If you were there for 12 minutes what would the fee be? $80

If you were there for 20 minutes what would the fee be? $80+$5(20-15) = $105


 
 

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